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The growing interest in soft robotics arises from their unique ability to perform tasks beyond the capabilities of rigid robots, with soft actuators playing a central role in this innovation. Among these, electromagnetic soft actuators (ESAs) stand out for their fast response, simple control mechanisms, and compact design. Analytical and experimental studies indicate that smaller ESAs enhance the force per unit cross-sectional area (F/CSA) without compromising force efficiency. This work uses the magnetic vector potential (MVP) to calculate the magnetic field of an ESA, which is then used to derive the actuator’s generated force. A mixed integer non-linear programming (MINLP) optimization framework is introduced to maximize the ESA’s F/CSA. Unlike prior methods that independently optimized parameters, such as ESA length and permanent magnet diameter, this study jointly optimizes these parameters to achieve a more efficient and effective design. To validate the proposed framework, finite element-based COMSOL 5.4 is used to simulate the magnetic field and generated force, ensuring consistency between MVP-based calculations and the physical model. Additionally, simulation results demonstrate the effectiveness of MINLP optimization in identifying the optimal design parameters for maximizing the F/CSA of the ESA. The data and code are available at GitHub Repository. 

In this paper, we present a novel means of control design for probabilistic movement primitives (ProMPs). Our proposed approach makes use of control barrier functions and control Lyapunov functions defined by a ProMP distribution. Thus, a robot may move along a trajectory within the distribution while guaranteeing that the system state never leaves more than a desired distance from the distribution mean. The control employs feedback linearization to handle nonlinearities in the system dynamics and real-time quadratic programming to ensure a solution exists that satisfies all safety constraints while minimizing control effort. Furthermore, we highlight how the proposed method may allow a designer to emphasize certain safety objectives that are more important than the others. A series of simulations and experiments demonstrate the efficacy of our approach and show it can run in real time. 

In this paper, we develop a novel and safe control design approach that takes demonstrations provided by a human teacher to enable a robot to accomplish complex manipulation scenarios in dynamic environments. First, an overall task is divided into multiple simpler subtasks that are more appropriate for learning and control objectives. Then, by collecting human demonstrations, the subtasks that require robot movement are modeled by probabilistic movement primitives (ProMPs). We also study two strategies for modifying the ProMPs to avoid collisions with environmental obstacles. Finally, we introduce a rule-base control technique by utilizing a finite-state machine along with a unique means of control design for ProMPs. For the ProMP controller, we propose control barrier and Lyapunov functions to guide the system along a trajectory within the distribution defined by a ProMP while guaranteeing that the system state never leaves more than a desired distance from the distribution mean. This allows for better performance on nonlinear systems and offers solid stability and known bounds on the system state. A series of simulations and experimental studies demonstrate the efficacy of our approach and show that it can run in real time. Note to Practitioners —This paper is motivated by the need to create a teach-by-demonstration framework that captures the strengths of movement primitives and verifiable, safe control. We provide a framework that learns safe control laws from a probability distribution of robot trajectories through the use of advanced nonlinear control that incorporates safety constraints. Typically, such distributions are stochastic, making it difficult to offer any guarantees on safe operation. Our approach ensures that the distribution of allowed robot trajectories is within an envelope of safety and allows for robust operation of a robot. Furthermore, using our framework various probability distributions can be combined to represent complex scenarios in the environment. It will benefit practitioners by making it substantially easier to test and deploy accurate, efficient, and safe robots in complex real-world scenarios. The approach is currently limited to scenarios involving static obstacles, with dynamic obstacle avoidance an avenue of future effort.